POST UTME REDEEMERS UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = \frac{1}{2} \log_{10} \( x^2 + 1 \) ) u\sing the chain rule.
A. \frac{1}{x^2 + 1}
B. \frac{1}{2} \cdot \frac{2x}{x^2 + 1}
C. \frac{x}{x^2 + 1}
D. \frac{1}{2} \cdot \frac{2x}{x^2 + 1} \cdot \log_{10} \( x^2 + 1 \)
Question 2
Find the magnitude of the vector $\vec{a} = \langle 3, 4 \rangle$.
A. 5
B. \sqrt{5}
C. \sqrt{10}
D. \sqrt{20}
Question 3
Solve for x in the equation \( 2^x + 2^{-x} = 5 \).
A. \( \log_2\( 3 \ \) )
B. \( \log_2\( 2 \ \) )
C. \( \log_2\( 4 \ \) )
D. \( \log_2\( 5 \ \) )
Question 4
A random variable X has a probability distribution given by \[ P(X) = \begin{cases} 0.2 & \text{if } X = 1 \\ 0.3 & \text{if } X = 2 \\ 0.5 & \text{if } X = 3 \end{cases} \]. Find the expected value of X.
A. 1.4
B. 1.7
C. 2.1
D. 2.5
Question 5
A quadratic equation has roots $\alpha$ and $\beta$ such that $\alpha + \beta = 3$ and $\alpha \beta = 2$. Find the equation of the quadratic.
A. x^2 - 3x + 2 = 0
B. x^2 - 3x - 2 = 0
C. x^2 + 3x + 2 = 0
D. x^2 + 3x - 2 = 0
Question 6
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of all students in the university.
A. 170.3 cm, 180.7 cm
B. 168.1 cm, 182.9 cm
C. 169.5 cm, 181.5 cm
D. 171.1 cm, 179.9 cm
Question 7
Find the area under the curve of \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. 0.7854
B. 0.4636
C. 0.5723
D. 0.6931
Question 8
Solve the quadratic equation \[ x^2 + 5x + 6 = 0 \].
A. -2
B. -3
C. -1
D. 4
Question 9
Evaluate the definite integral \( \int_{0}^{1} x^2 \, dx \).
A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{1}{2}
D. \frac{1}{4}
Question 10
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24
B. 62.83
C. 78.54
D. 100.53
Question 11
Find the equation of the line pas\sing through the points (2, 3) and (4, 5) in the coordinate plane.
A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 1
D. y = -2x - 1
Question 12
A random variable X has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \cdot \frac{1}{x^2} ) for \( x = 1, 2, 3, 4, 5 \). Find the probability that X is greater than 3.
A. \frac{1}{2}
B. \frac{1}{4}
C. \frac{1}{8}
D. \frac{1}{16}
Question 13
Solve the system of equations \begin{align*} x + y &= 4 \ x - y &= 2 \end{align*}.
A. \{(2, 2)\}
B. \{(2, 3)\}
C. \{(3, 1)\}
D. \{(4, 0)\}
Question 14
Find the equation of the line pas\sing through the points $\( -2, 3 \)$ and $\( 1, -2 \)$.
A. y = -\frac{5}{3}x + \frac{13}{3}
B. y = \frac{5}{3}x - \frac{13}{3}
C. y = -\frac{3}{5}x + \frac{13}{5}
D. y = \frac{3}{5}x - \frac{13}{5}
Question 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)

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